Year: 2017
Type: preprint
Abstract: Sub-Riemannian cubics are a generalisation of Riemannian cubics to a sub-Riemannian manifold. Cubics are curves which minimise the integral of the norm squared of the covariant acceleration. Sub-Riemannian cubics are cubics which are restricted to move in a horizontal subspace of the tangent space. When the sub-Riemannian manifold is also a Lie group, sub-Riemannian cubics correspond to what we call a sub-Riemannian Lie quadratic in the Lie algebra. The present article studies sub-Riemannian Lie quadratics in the case of $\mathfrak{su}(2)$, focusing on the long term dynamics.
Source: arXiv (Cornell University)
Authors: Swaddle, Michael, Noakes, Lyle
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2774980483